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simplification of sums


hi,

i'm using Mathematica and would like to manipulate various symbolic sums. in particular,
given that Xbar=Sum[X[i],{i,n}]/n, i would like to be able to simplify 

Sum[(X[i]-Xbar)^2,{i,n}] to Sum[X[i]^2,{i,n}] - n Xbar^2

also, i would like to be able to distribute summation in general:

Sum[a + b - c,{i,n}] -> Sum[a,{i,n}] + Sum[b,{i,n}] - Sum[c,{i,n}]

and pull constant factors out of the sum

Sum[2 a X[i],{i,n}] -> 2 a Sum[X[i],{i,n}]

i've tried to write my own Rules for ReplaceAll, but without success. the package
Algebra`SymbolicSum` does not seem to help.

any suggestions out there?

bob

-- 
Dr. Robert B. Nachbar | Merck Research Laboratories | 908/594-7795
nachbar at merck.com     | RY50S-100                   | 908/594-4224 FAX
                      | PO Box 2000                 |
                      | Rahway, NJ 07065            |






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